Thursday, December 12, 2013

Battery History

The following are notes on battery history
  • History of Batteries
    • 2000 years ago Baghdad battery
      • created in Mesopotamia 
      • Jar of ceramics created with a speculated structure of copper with walls of iron
      • if filled with unknown composition of electrolytes meets the requirements for a battery
      • Maybe used to plate gold onto silver?
    • 200 Years Ago Animal Electricity
      • Galvani while doing a dissection a steel scalpel touched a brass hook that was holding a frog leg in place
      • Battery composition
        • Steel scalpel has iron 
        • brass hook has copper
        • preservatives acted as electrolytes
  • First Battery
    • Voltaic Pile 
    • set of individual galvanic cells placed in series
    • copper and zinc stacked together with electrolytes sandwiching the two metals
  • History of electrochemical energy storage
    • Galvani
    • Volta - Voltaic Pile 
    • Daniell - Zn/Cu Cell
    • Faraday - Basic Principles of electrochemistry
    • Grove - H2/02 cell
    • Plante - Lead Acid Cell
    • Leclanche - Zn Carbon dry cell
    • Edison Zn/Ni and Fe/Ni cells
  • Modern Batteries
    • modern development started around half a century ago
    • Solid Electrolytes
      • 1966 Yao and Kummer Beta Alumina Solid Electrolyte: Fast Na Ion Conductor
      • birthed solid state ionics
      • Rubidium silver iodide
    • Internal Phenomena
      • Whittingham steele insertion reaction electrodes
      • created Le/TiS2 cells
      • Sony commercialized the first Lithium ion batteries

Friday, December 6, 2013

Notes - The ElGamal Public Key Cryptosystem

The following are notes from Introduction to Cyrptography with Coding Theory.
  • ElGamal Public Key Cryptosystem
    • Alice wants to send a message m to Bob
    • Bob chooses a large prime p and a primitive root α
    • Bob chooses a secret integer a and computes B ≡ α (mod p)
      • Make public (p, α, B) and is Bob's public key
    • Alice
      • downloads (p, α, B)
      • Chooses a secret random integer k and computes r ≡ α (mod p)
      • Computes t ≡ B k m (mod p)
      • sends the pair (r,t) to B
    • Bob decrypts by computing tr -a ≡ m (mod p)
  • Security
    • depends on a being kept secret which is reliant on the idea that discrete logs are difficult to compute

Notes - Discrete Logarithms

The following are notes from Introduction to Cyrptography with Coding Theory.

  • RSA Algorithm relies on the difficulty of factoring, but we can also use the difficulty of discrete logs
  • Fix a prime p. Let α and Β be nonzero integers mod p and suppose
    • Β ≡ αx (mod p)
  • It is difficult to find x assuming we choose a large enough prime
  • α is taken to be a primitive root mod p so that every Β is a power of α (mod p)
  • The size of the largest primes for which discrete logs can be computed is usually about the same size as the largest integers that could be factored
  • This means that discrete logs are another example of one-way functions
    • where f(x) is easy to compute but given y it is computationally infeasible to find x

Thursday, December 5, 2013

Notes - An Application to Treaty Verification

The following are notes from Introduction to Cyrptography with Coding Theory.
  • This method will essentially describe the RSA signature Scheme
  • Example
    • Countries A and B have signed a nuclear test ban treaty
    • Country A wants to verify the treaty by placing sensors in B
      • Country A wants to ensure sensors are sending correct data without tampering
      • Country B wants to look at the message before its being sent to ensure that espionage data is not being transmitted
    • A chooses n = pq to be the product of two large primes and chooses encryption/decryption exponents e and d
    •  n and e are given to B but p q and d are kept secret
    • sensor collects data x and uses d to encrypt x to y ≡ xd (mod n)
    • both x and y are sent to country B to check that ye ≡ x (mod n) and then to Country A to ensure that the number x has not been modified. If x was modified it would be the same difficulty as decrypting the rsa message x

Notes - The RSA Algorithm

The following are notes from Introduction to Cryptography with Coding Theory.
  • Public Key Cryptosystem
    • Presented by Diffie-Hellman
    • Goal - allow Alice to send a message to Bob without previous contact and without the use of a courier to exchange a key but protect the message from Eve a potential attacker
  • The RSA Algorithm
    • Bob chooses secret primes p and q and computes n = pq
    • Bob chooses e with gcd(e, (p-1)(q-1)) = 1
    • Bob computes d with de ≡ 1 (mod(p-1)(q-1))
    • Bob makes n and e public, and keeps p, q, d secret
    • Alice encrypts m as c ≡ me (mod n) and sends c to Bob
    • Bob decrypts by computing m ≡ cd (mod n)
  • Example of the RSA Algorithm
    • p = 885320963, q = 238855417
    • n = p * q = 211463707796206571
    • Let the encryption exponent be e = 9007
    • Let the sample message m be 30120
    • c  ≡ me ≡ 301209007 ≡ 113535859035722866 (mod n)
      • Where c stands for the ciphertext Alice is sending to Bob
    • Bob knows p and q so he knows (p-1)(q-1) then he uses the extended euclidean algorithm to compute d such that de ≡ 1  mod (p-1)(q-1)
    • d = 116402471153538991
    • Bob computes cd ≡ 113535859035722866116402471153538991 ≡ 30120 (mod n) to obtain the original message